Math 417 is an introduction to abstract algebra. The main objects of
study are groups, which are abstract mathematical objects
that reflect the most basic features of many other mathematical
constructions you are likely familiar with. Rather than beginning
our discussion with groups, we will instead
spend some time discussing more familiar
algebraic structures, namely fields, polynomials, and vector spaces.
After sufficient motivation, we define groups and begin their
systematics study. If time permits, we will discuss some deeper
connections between group theory, fields and polynomials.
The goal of the course is to introduce the students to abstract
mathematical thinking through the study of these simple, beautiful
mathematical constructions, and to explore the relationship to other
areas of mathematics.
The text for this course is an expansion of the instructors lecture
notes.
More and more of the text will become available
here,
as it is updated throughout the semester. Please report any errors to
me.
I will not cover everything from these lecture notes in class, and I will
assume that you have read everything from the sections covered,
even if they were not discussed in class. This is crucial since class
time is extremely limited. As an additional
reference, one can use
Frederick M. Goodman, Algebra: Abstract and Concrete (Edition 2.6), SemiSimple Press Iowa City, IA.
(available online free here).
or the book at the bookstore:
John B. Fraleigh, A First Course in Abstract Algebra
Grades will be based on
Weekly homework (15%): This will be assigned at the
beginning of the week, covering the material for that week, and will be
due the following Tuesday or Thursday with a few exceptions (as posted).
This will be
graded by the grader.
Quizzes(5%): There will be short quizzes
(at most one
per week), typically on Thursday. This is to check that you know
the absolute basics of what we are doing in class. It will typically
cover very recent material, or if reading was assigned, it may cover
that.
Super-quizzes: There will be three "super-quizzes" near
the end
of the semester, each of which will count as ONE extra credit point toward
the final exam. One point will be awarded ONLY if the solution is
completely correct. There is no penalty for missing the super-quiz or
failing to provide a completely correct solution. There are no
make-ups.
Three in-class midterms (10%,20%,20%):
These will be held Feb. 4, March 8, and April
12.
Final exam (30%):
This will be a 3
hour exam held 7:00--10:00pm, Thursday, May 12.
There will be a take home portion of the final exam, handed out on
the last day of class.
Videos of lectures: These are now available here (you
will need to log in with your NetID and password).
Assignments (please report any errors/mistakes to me)
Note: Illegible work will be returned, ungraded.
All assignments will come from this text.
HW1: Do all problems from section 1.1, 1.2, and 1.3. Turn in problems
1.1.1, 1.2.2, 1.2.3, 1.2.4, 1.3.1, 1.3.2. Due 1/26, beginning of
class.
HW2: Do all problems from section 1.4 and 1.5. Turn in problems
1.4.2, 1.4.3, 1.4.4, 1.5.2, 1.5.3, 1.5.4. Due MONDAY 2/1, by 4:00pm
(in my office, 366 AH).
HW3: Do all problems from section 2.1, 2.2 and the first two from 2.3.
Turn in problems 2.1.1, 2.1.2, 2.2.1, 2.2.2, 2.3.1. Due Tuesday 2/16,
beginning of class.
HW4: Do the rest of the problems from section 2.3 and all problems
from section 2.4. Turn in problems 2.3.3, 2.3.4, 2.3.6, 2.4.3, 2.4.5.
Due
Tuesday, 2/22, beginning of class.
HW5: Do all problems from sections 2.5, 2.6, as well as problems
3.1.1 - 3.1.4 from section 3.1. Turn in 2.5.1, 2.5.4, 2.6.3, 2.6.4,
3.1.1, 3.1.3. Due Tuesday, 3/1, beginning of class.
HW6: Do the rest of the problems from section 3.1 and all problems
from section 3.2. These will not be turned in, but you will be
responsible for them on the midterm.
HW7: Do all problems from section 3.3, problems 3.4.1-3.4.5 from section
3.4. Turn in 3.3.1, 3.3.4, 3.3.6, 3.3.8, 3.3.10, 3.4.1, 3.4.2, 3.4.4, due Thursday 3/17.
HW8: Do and turn in problems 3.4.3, 3.4.6, 3.4.7, 3.4.8, due Tuesday 3/29 (first Tuesday after spring break).
HW9: Do all problems from section 3.5 and 3.6.2-3.6.4 from 3.6. Turn
in problems 3.5.1, 3.5.4, 3.5.6, 3.6.2, 3.6.3, 3.6.4, due Tuesday, 4/5,
beginning of class.
HW10: Do the rest of the problems from section 3.6 and all problems
from section 3.7. These will not be turned in, but you will be
responsible for them on the midterm.
HW11: Do all problems from Section 4.1 and turn in 3.7.6, 3.7.8,
4.1.1, 4.1.3, 4.1.4, 4.1.6, due Wednesday, 4/20, by 10:00am (in my
mailbox).
HW12: Do all problems from Section 4.2 and 4.3.1-4.3.6. Turn in
4.1.9, 4.2.3, 4.2.8, 4.3.1, 4.3.4. Due Wednesday, 4/27, by 10:00am
(in my mailbox).
HW13: Do all problems from Section 4.3 and 5.1. Turn in 4.3.6,
4.3.8, 4.3.9, 5.1.2, 5.1.3, 5.1.5. Due Wednesday, 5/4, by 10:00am (in my
mailbox).
Note: The
online version of the text is now complete
through section 4.2. The online version is the definitive version for
homework problems.
Week 12: Midterm 3 (Section 3.3-3.7), Tuesday 4/12. Reread Section
3.7 and Section 4.1 for Thursday.
Week 13: Read Section 4.2 and 4.3.
Week 14: Read Section 4.3 and 5.1.
Week 15: Read Section 5.1 and 5.2.
Other things
The first midterm on 2/4, will cover everything from Chapter 1. That
is the third week of class!
The reviews are at the end of each section in the form of the "You
should..." list.
I am away 2/3-2/4, and in particular office hours will be reschedule
for that week as follows: Monday 12-2, Tuesday 8:30-9:30, Wednesday
8-9:30.